Phase locked states

by Judith Curry
Of relevance to our discussion on the Tsonis et al papers and spatio-temporal chaos, there is a new paper out by David Douglass in Physics Letters, entitled “Topology of Earth’s climate indices and phase-locked state.”
Topology of Earth’s climate indices and phase-locked state
David H. Douglass
Physics Letters A (August 2010)
Phase-locked states in Earth’s climate system were identified in a study of a set of climate indices by Swanson and Tsonis (2009) [1] (ST). They reported five climate shift events since 1900 based upon fea- tures in a phase-locking parameter S. The present study finds that sets of climate indices have important topological properties such as a metric diameter D that describes the magnitude of phase locking among the indices. Minima in D as a function of time are shown to be associated with climate shifts. Eighteen strong events since 1870 are identified, including the five reported by ST. Ten of these minima corre- spond to reported events such as the well documented “climate shift of the mid-1970s” and the more recent climate shift of 2001–2002. Most climate shifts tend toward radiative equilibrium. 

Link to the paper is here.

Does 18 climate shifts since 1870 make sense from Douglass argument?  He asks the question as to what is causing the climate shifts.  He suggest one possibility as being strong short-duration events such as volcanoes, but this certainly does not answer all of the related questions.

This statement caught my eye:

That AMO lags the Pacific indices by 7 to 9 months suggests that the climate shifts originate in the Pacific. Additionally, within the Pacific indices Nino3.4 sometimes leads, suggesting that those events originate in the Tropical Pacific. These questions should be studied for each climate shift listed by varying lag times and different geographic sets of indices.

I think I have come across this idea before of a relationship between the AMO and the PDO, but I’m not sure where?


80 responses to “Phase locked states

  1. As an electronics guy i love phase locked loops and their real world applications.
    i did my best to read his article but it’s more high falutin’ mathematics than nuts&bolts technician stuff on which i thrive…

    But it’s encouraging to see this kind of analysis applied too climate for when they look at the right things the math will show they’ve found them.

    Compare that to studying computer models, which let’s face it are figments of imagination and can demonstrate only that some idea is plausible and nothing more.

    Phase locked loop science applied to climate is wonderful in that it’ll seek out interrelationships that are not obvious. I’d love to see them incorporate some of Eschenbach’s thoughts in their investigation.

  2. As an electronics guy i love phase locked loops and their real world applications.
    i did my best to read his article but it’s more high falutin’ mathematics than nuts&bolts technician stuff on which i thrive…

    But it’s encouraging to see this kind of analysis applied to climate for when they look at the right things the math will show they’ve found them.

    Compare that to studying computer models, which let’s face it are figments of imagination and can demonstrate only that some idea is plausible and nothing more.

    Phase locked loop science applied to climate is wonderful in that it’ll seek out interrelationships that are not obvious. I’d love to see them incorporate some of Eschenbach’s thoughts in their investigation.

  3. Alexander Harvey

    Much as I did not like the way Tsonis handled phase and coupling it did try to demonstrate that a degree of enhanced predictability in phase component sexisted due to locking when the synchronisation was high and hence some realistic locking phenomenon was apparent during the climate shift events.

    I can not see how in this new paper the synchronisation is claimed as phase locking, in the Tsonis paper the increased predictability played that role, so I prefer the Tsonis paper, albeit with the note that I think it could have been improved if a more logical phase predictor had been used.


    • Alex – I hope Judith Curry will forgive me for a very temporary off-topic comment, but since you are online, I thought you might be interested in two papers that have appeared in JGR (oceans) over the past 30 days related to the role of deep ocean warming in contributing to the OHC budget. I believe these complement an earlier paper by Purkey and Johnson on the same topic.

      Sorry for the interruption. Back to phase locking and climate shifts.

      • Alexander Harvey

        Thanks Fred,

        I went to the site but I think they are pay for, and I do a very good church mouse impersonation.

        While you are here, can you tell me the difference between a paper and a “letter” in terms of review statndards, if any? For what it is worth I would like to see their “phase locking” challenged as I can not see it to be more than times when the data is looky-likey. The concept of the series locking phase together into a temporary regime running in lock step does not seem to be shown.

        I feel that papers/letters like these are more influential than they should be unless they are wrung inside out. The mathematics may look unfamiliar to some but as I see it all they have done is take the row minimum of the correlation matrix after dropping the diagonal and lagging a compnent or two. I am not sure how a fleeting correlation gets raised to a climate event.

        It might be good if they were taken to task, but that was a review issue hence my question about letters vs papers.


      • Alex – Although I don’t feel terribly well qualified to judge their approach, my reaction is similar to yours. Am I missing something, or is their definition of a “climate shift” somewhat circular, in that they define it as an occasion when their topological diameter D is less than 53 degrees, and then use that criterion to state that climate shifts occurred when the criterion was met? What I didn’t see was an independent description of what was shifted (except for references to an asserted few such shifts). I had the impression that the answer for some of the 18 occasions was “not much”. On the other hand, they acknowledged that if they made the criterion more stringent (narrowing the distance further below 53), they would miss some “real” climate shifts, again suggesting that the correlation between their definition and observable climate events was less than strong.

        I really don’t know how particular journals manage the distinction between letters and papers. It’s not the same for all journals.

  4. oops double post – can a moderator remove first one? it has typo…

    sorry, a.

  5. Interesting paper. It strikes me as inherently plausible that the majority of shifts have tended toward radiative equilibrium.

    One piece of complexity involving the proposed Pacific/Atlantic lag is one observation suggesting the converse on at least some time scales, such that Atlantic warming can enhance the easterlies that drive La Nina cooling in the tropical Pacific –

    Tropical Pacific Response to Atlantic Warming

    • David L. Hagen

      Judith & Fred
      Douglass: “It is suggested that even though there are only the three examples from DK that most of the shifts in Earth’s climate system are toward radiative equilibrium.”

      Ferenc Miskolczi 2007, 2010 also came to that conclusion in his 1D climate model, from an entropy production maximization method.

  6. Didn’t you allude to such a relationship in a discussion of Alaskan climate and models in 2003?

  7. Seen before, as in Tisdale ( I’m hoping this is the reference Pooh, Dixie intended in

  8. Judith wrote, “I think I have come across this idea before of a relationship between the AMO and the PDO, but I’m not sure where?”

    The detrended SST anomalies of the North Pacific (north of 20N) and of the North Atlantic (the AMO) run in and out of synch, or at least they have since the start of the HADISST dataset:

    The graph is from my Intro to the PDO post:

  9. Does anyone else have problems with the first page of this link? It’s a blank page.

    Click to access Topology_PLA20011.pdf

    Without the definitions of the datasets, there’s no reason to read the rest of the paper.

    • “Does anyone else have problems with the first page of this link? It’s a blank page.”

      I had to scroll all the way through the paper, and then back to the first page. It filled out when I did that.

    • Bob,
      I very briefly had the first page of D.H. Douglass / Physics Letters A 374 (2010) 4164–4168 on Elsevier but not long enough to capture. There is a screen shot of the first page at Deepdyve. Others are pay-walled. Sounds interesting. There is no shortage of smear campaigns against Douglass.

  10. Thanks for an unbiased website.

    They seem to look for too hard for patterns in the noise. What would account for this and how would this regualr periodicity always work despite huge variation is aerosols in the atmosphere, solar cyles, etc.

  11. here is the link to the paper again, is this not working, is working for me:

    Click to access Topology_PLA20011.pdf

    note the link is on the 2nd line of my post, is there a problem with the link?

  12. Initial notes/question about Douglas 2010:

    The paper states, “AMO are the monthly temperature anomalies of the Northern Atlantic Ocean (latitudes: 0 to 70N). These are calculated from the Kaplan SST data set from 1856 to present. See Enfield et al. [10].”

    A clarification: Reference 10 was a link to the ESRL AMO data which is detrended North Atlantic SST anomalies, not the “monthly temperature anomalies of the Northern Atlantic Ocean” as stated.

    The South Pacific dataset (SPC1) is based on HADISST data. The vast majority of HADISST South Pacific SST data is infilled prior to the satellite era (1982 to present) so the Principal Component analysis of this dataset is basically an analysis of infilling methods used by the Hadley Centre.

    So the paper is analyzing one raw Kaplan-based SST dataset (NINO3.4), one detrended Kaplan-based SST dataset (AMO), and two datasets (NPC1 & SPC1) based on principal component analyses of HADISST-based SST datasets, one of which is ultimately based on little source data. Why is there a mix SST datasets? And why is raw & detrended SST data analyzed alongside two PC-based datasets? Why not simply detrend the North and South Pacific SST data as was done with the North Atlantic SST anomalies to create the AMO?

  13. Was this the episode where Jordie and Wes had to do something innovative?

  14. The choice of D is arbitrary, I guess it makes sense as a starting point, but it looks like a narrow range of D may make more. His definition of “Climate Shift” is confusing, climate shift potential trigger? I am not familiar with the all the data. It may be interesting, but I would wait on the paper and discussion following.

  15. the well documented “climate shift of the mid-1970s” and the more recent climate shift of 2001-2002.

    True, but add 1880, 1910 & 1940 to the list.

    The complete list is [1880, 1910, 1940, 1970, 2000, 2030, 2060, etc]

    Here is what the data says:

  16. Dr. Curry,
    Another interesting aspect of climate shifts is the possibility of solar influence. Unfortunately, the only paper I have seen on it is behind a pay wall.

    It might be an interesting blog topic in the future.

    • The connection of the Southern Annular Mode and ENSO is well established – see for instance – although there are many others.

      Judith Lean (2008) commented that ‘ongoing studies are beginning to decipher the empirical Sun-climate connections as a combination of responses to direct solar heating of the surface and lower atmosphere, and indirect heating via solar UV irradiance impacts on the ozone layer and middle atmospheric, with subsequent communication to the surface and climate. The associated physical pathways appear to involve the modulation of existing dynamical and circulation atmosphere-ocean couplings, including the ENSO and the Quasi-Biennial Oscillation. Comparisons of the empirical results with model simulations suggest that models are deficient in accounting for these pathways.’ One of the ‘physical pathways’ seems to involve UV warming of ozone and changing downwelling in the polar vortices.

      Click to access ndx_lean.pdf

      Lockwood et al (2010) discussed top down forcing by solar UV in the Northern Hemisphere – although it is equally applicable in the south. ‘During the descent into the recent exceptionally low solar minimum, observations have revealed a larger change in solar UV emissions than seen at the same phase of previous solar cycles. This is particularly true at wavelengths responsible for stratospheric ozone production and heating. This implies that ‘top-down’ solar modulation could be a larger factor in long-term tropospheric change than previously believed, many climate models allowing only for the ‘bottom-up’ effect of the less-variable visible and infrared solar emissions. We present evidence for long-term drift in solar UV irradiance, which is not found in its commonly used proxies.’

      The Antarctic Circumpolar Current is the strongest ocean current on Earth. In particular, it flows from west to east through the narrows of Drake’s Passage between the Antarctic Peninsula and the southern tip of South America. A positive SAM index is by convention lower sea level pressure at the pole and higher pressure at lower latitudes. Storms remain in the south and Southern Ocean water pushes strongly through Drake’s Passage. A negative SAM is the reverse and results in storms and cold water pushing into lower latitudes. Note the negative SAM as of January 2010 –

      Cold water pushing up from Antarctica can be seen here in January 2010 – A cold pool has formed off the South American coast in the region of the Humboldt Current.

      In this area, cold and nutrient rich upwelling sub surface currents are sometimes suppressed by a warm surface layer and sometimes surface strongly in the most productive ecosystem on Earth. The Humboldt current is the thermal origin of ENSO. A good introduction is provided by the National Ocean and Atmospheric Administration (NOAA) at their LME website –

      Once cold water starts to upwell – the cold tongue moves eastward across the Pacific driven by planetary rotation and reinforced by wind and cloud feedbacks.

      The influence of solar UV on ENSO is supported both by correlation and with a plausible physical connection through UV warming of ozone, Polar and sub-Polar sea level pressure and Southern Hemisphere storm tracks.

      The UV origin of ENSO poses some very interesting questions about just where global surface temperatures might be heading longer term – with the prospect of a Maunder Minimum around the corner.

      • Chief,

        if thermal modulations of ocean current in the southern hemisphere can be tracked back to Antarctica (which is what I think you are saying) and the variation in UV and near-UV drive variations in ocean heat content, can we see an effect of a thinner ozone layer over Antarctica in the modulation of southern ocean heat content or events related to southern ocean heat content?

      • Maxwell,

        The thermal origin of ENSO is in super cold and nutrient rich upwelling in the eastern Pacific. These upwelling currents are suppressed by a warm surface layer or upwell strongly through cooler surface water. Cold currents spinning (Ekmann Flow) off the circumpolar current are a determinant of surface water temperature off the western coast of South America.

        Changes in solar UV drives changes in heat content of the middle atmosphere and ozone layer. This in turn affects downwelling of cold air in the polar vortex and sea level pressure in Polar and sub-Polar regions- as measured by the Southern Annular Mode index.

        There is no direct effect on ocean heat content – the UV component of solar irraddiance being very small in energy terms compared to the infrared and visible components. But it is absorbed by and warms ozone in the middle atmosphere which influences sea level pressure at the poles. These sea level pressures drive rainfall and temperature in the Southern Hemisphere. There are feedbacks from ENSO involving cloud which strongly influence ocean heat content.

        ‘Cold-core cyclones occur in higher latitudes and draw energy from the Arctic and Antarctic regions. Polar vortexes are huge cyclones in northern latitudes that measure more than 600 miles across near the poles. These cold-core cyclones can cause blizzards on land or savage storms at sea. As their strength grows and wanes, smaller Polar lows spin off and drift into the middle latitudes to become extra-tropical.’

        Here is a very Australian take on SAM

        See also –

        Here is the AR4 graph of SAM –

        The positive trend seems to have peaked in the late 1990’s – although it is currently positive explaining the reduced rainfall this year in Southern Australia.

        UV influences waxing and waning of the Polar Vortex – and feeds into cold currents moving up the coast of South America. Ozone loss is another and quite different question. The typical estimate is to put 50% of recent change in SAM to ozone loss – I have my doubts.


      • Chief,
        Thank you for the lengthy and thoughtful reply. There is so much in your comments, it is hard for me to catch up. I have some reading to do now. I am looking for good science papers that describe natural climate variability so I appreciate these links.

      • Ron

        It is my pleasure entirely to collaborate with a fellow seeker of the sacred hydrological truth. Many people think they understand everything in the Universe – climate amongst other things. We tell ourselves some simple story and think we have an eternal truth.

        Most amusing – things are always more complex. To paraphrase the Hitchhikers Guide climate is: ‘more complex than the most complex thing ever and then some. Much more complex than that in fact, really amazingly complex, a totally stunning complexity, a “wow, that’s complex”, time. Climate is just so complex that by comparison, complexity itself looks really simple. Amazing multiplied by intricate multiplied by staggeringly complex is the sort of concept we’re trying to get across here. ‘


  17. just resubscribing :)

  18. Dr. Curry,
    Regarding the PDO influencing a shift in the NAO, it is possible it was discussed in the following paper. I have not read the whole paper, only glimpses, but it looks to be relevant as it is discussing oceanic oscillations and teleconnections.

    It was definitely discussed in this paper, again behind a pay wall.

  19. Dr. Curry

    I think I have come across this idea before of a relationship between the AMO and the PDO, but I’m not sure where?

    I believe I shotgunned a batch of references to Bob Tisdale’s marvelous animations at the following topic on Climate Etc.
    Ellison, Robert. 2011. Decadal variability of clouds. Scientific. Climate Etc. February 9.
    Specifically, here and on several subordinate replies.

    I was particularly struck by the animation of a cool ENSO phase into the East Indian Ocean and the Northern Atlantic Ocean.

    • Sorry, the bolding was supposed to have been turned off following the word “here”. :-(

  20. Pooh, Dixie

    Being a bear of very little brain, I took away a notion from the animations, text, and NOAA diagrams, which as I state it, is almost guaranteed to be wrong: The globe has a strong self-regulating mechanism that operates to keep heat content within a range.
    1) The sun heats the Nino 3.4 block in the Pacific (and elsewhere).
    2) Rising heated air gives rise to easterly trade winds.
    3) Trade winds blow a heightened warm pool westward. The weight of the warm pool pushes the thermocline down.
    4) The cool water under the thermocline is sloshes eastward and closer to the surface (La Nina).
    5) La Nina propagates, with lags, to other ocean basins. (Fish and fishermen change their hunting grounds.)
    6) The warm pool, meanwhile, generates high Cumulus/Cumulonimbus clouds producing rain and releasing heat to space (Iris effect).
    7) The Warm Pool cools.
    8) The Trade Winds moderate.
    9) The water and the Thermocline sloshes back, as surveyors say, to the point of beginning.

    Since my description above is almost surely botched, I’ll leave it to other students of climate to set me right. After all, the ideas were theirs to begin with. I just mangled them.

    • Dear Pooh

      “Oh Dear Ooh gracious this all comes from eating too much.”

      Perhaps I can add to the analysis.

      The underlying essential condition for much of climate is planetary rotation. It is so fundamental yet barely mentioned – it provides the conditions for most of the variations we see. It is certainly the case for ENSO – so much so that La Niña is often considered to be the default condition. If nothing else happened the rotation of the planet would see easterlies blowing across the equatorial Pacific pushing warm surface water up against Australia and Indonesia. For a La Niña to form we need upwelling of super cold subsurface water in the region of the Humboldt current. This is where global oceanic currents most strongly upwell. The oceanic currents are commonly represented as a conveyor belt. Too simple by far – think instead turbulent washing machine and not a quiet meandering stream.

      Currents upwell on the margins of land masses dependent on the direction of surface winds. The Humboldt Current – and therefore ENSO – is the result of globally very significant upwelling on the western coast of South America – but there is also a very significant area of upwelling on the western coast of North America which feeds into the PDO.

      As the super cold and nutrient rich water rises – it is pushed north and west across the central Pacific by the trade winds. The warm water pushed to west warms the air above it which rises strongly creating low pressure systems that strengthen the trade winds. Warm water pushes through between Australia and Indonesia warming the eastern Indian Ocean. Clouds forming above the cool central Pacific are pushed westward towards the low pressure zones to Australia, Asia, India and Africa.

      Upwelling varies on interannular to decadal to millennial timescales bur something happens fairly regularly to reduce upwelling in the eastern Pacific – the upwelling is the key to ENSO and the PDO. The typical explanation involves Rossby Waves –

      The result is that the warm pool in the western Pacific spreads eastward in an El Niño. A common misconception is that we get more evaporation from warm water. What happens is that there is very quickly higher temperature and moisture content in the air above and less evaporation – this is known as the evaporation paradox. The trade winds also are diminished again reducing evaporation. However because warm water in an El Niño spreads out over such a vast area – the net (rather than the point) evaporation is greater and this feeds into the hydrological cycle as increased global precipitation and especially in North and South America.

      It is a little more difficult to explain multi-decadal aspects of Pacific Ocean phenomenon by Rossby Waves – perhaps some harmonic oscillation is involved. The ideas of solar UV mediated changes on interannular to millennial timescales to ocean and atmosphere coupling can’t be discounted.

      With ENSO and the PDO – it all starts with upwelling on the western margins of the Americas. This is sometimes suppressed by a warm surface layer 100m or so deep and sometimes not.


  21. Re: AMO and PDO, yes, the d’Orgeville and Peltier paper discusses this (doi:10.1029/2007GL031584). To some extent Zhang and Delworth (doi:10.1029/2007GL031601) also propose this.

  22. Tomas Milanovic

    A rather thin paper for me.
    What is the difference between Douglas and Tsonis?

    Douglas significantly improves the phase and distance with regard to the somewhat arbitrary and qualitative Tsonis definitions.

    Douglas’ di,j = Arccos(ρi,j).
    ρi,j is well defined (Pearson coefficient) and represents a cos of an angle.
    So di,j is indeed a phase.
    Then D(I0,t) is a true metric space what is a good thing too.

    On the other hand Tsonis has used 2 parameters while Douglas uses only 1. Tsonis uses first a “phase” on which Douglas significantly improves then this ill named “coupling” which was in fact just a measure of a the relevance of a linear predictor.
    In a way Tsonis analysis imposed 2 times more constraints on the index space so he found 2 times less “events”.

    A major difference is also in the definition of the “events”.
    While Tsonis makes an effort to define an “event” as a significant change in ENSO variability, Douglas never defines what a “climate shift”is – yes he writes it with “.

    Then we have just a little algebra (computing the Pearson coefficients for a moving window of 7 years (!) like Tsonis) and plotting the max(di,j) which he calls “topological diameter” with time.
    As this gives necessarily wriggles, there are minima and maxima.
    The minima correspond to a position of the window where the least square lines of the indexes are rather parallel and are conventionally put in the MIDDLE of the 7 years window.
    In other words , when the indexes went roughly in the same direction during 7 years, then the date in the middle of these 7 years will show a minimum “topological diameter”- TD.

    Last, somewhat circularly Douglass assimilates a “climate shift” at date t with the minimum of the TD at date t.
    We’ll never learn in the paper what really happened at those 18 or so minima.
    Of course the Tsonis’ “events” are a subset of Douglas’ “climate shifts” because it is basically the same method with Tsonis constraining the system 2 times more.

    My comments:

    – 18 “climate shifts” in only 140 years is much too much to deserve the term “shift” implying something important, new and significant. So while the method, perhaps, finds something, this something is probably banal and short term.

    – it is neither justified why the TD is taken in the middle of the window (so its value depends on the future) nor why it should be 7 years. To be fair Douglas says in the conclusion that the windows should be varied. I add that the position of TD in the window should be justified too.

    – the plots depend critically on assumed lags between the indexes. Douglas says too that this should be analysed.

    – I left the most important for me the last. The set of the indexes is arbitrary.
    There is no reason to take 3 rather than 8.
    Or even 23 by constructing other indexes on different spatial partitions.
    This comment comes from abundant experience with EOF.
    Indeed the EOF method is known to be extremely vulnerable to the definition of spatial domain.
    When one gets an EOF study, the first thing to do is to cut the space domain in 2 or 3 and/or translate-reduce-expand it and redo EOF for each piece.
    This test immediately shows if the findings were artefacts of an arbitrary domain definition or if there perhaps is something.
    You would be surprised how often people don’t do this fundamental check.
    The same is true for the index sets even if they are not properly speaking exactly EOF methods.
    Again to be fair, Douglas writes in the conclusion : “These questions should be studied … by different geographic sets of indices “.
    So he is aware of the of the problem.

    In any case the size and the importance of the problems to be solved that Douglas lists in the 4.5 “Future studies” shows how tentative and preliminary this paper is. Personnaly I wouldn’t accept it for publication untill these questions are better analysed but that’s just me.

  23. When the cause is not clear or known, ‘playing’ with the de-trended consequences only muddies the waters. Both the North Atlantic and North Pacific are driven by independent forces, which on decadal scale get in and out of phase (see B. Tisdale’s comments), but in longer term appear to have a common cause, if jugged by the inclination of the appropriate trend lines. This is no feedback of any kind, positive, negative, amplitude and specifically not any kind of the phase locked loop (I should be well familiar with).
    The paper in question may be an interesting academic exercise, but in my view of no practical value, or even a setback for the climate science, if taken seriously.

  24. david douglass

    Let me answer some questions and make a few comments:

    The four data sets in the Swanson and Tsonis paper were all in the northern hemisphere. In an effort to be more “global” my four included the southern hemisphere. Bob Tisdale asks “Why not simply detrend the North and South Pacific SST data… “ Answer: these data sets are detrended. Also I did an incomplete analysis with more indices and got essentially the same results.

    I agree that this paper leaves many unanswered questions. To encourage others to pursue this new approach I enumerated many of them. I am doing so myself in regard to the nature of the shifts. In the paper I pointed out that shifts #6 and #7 correspond to the beginning and ends of a time-segment showing 4 oscillations of period 3-years from 1896 to1908. I have found that there are many more time-segments showing n-year oscillations, where n=2 or 3, and where the beginning and end correspond to pairs of the shifts reported in this paper. For example, from 2001 to 2008 the data show oscillations of period 2-years.

    I will be glad to answer any questions that anyone raises.

    David Douglass
    Department of Physics
    University of Rochester

    • David,
      How do these 2 or 3 year oscillations relate to the multidecadal climate regime shifts? I normally think of a climate shift to warm in 1910, shift to cool in 1945, shift to warm in 1975/76, and shift to cool in 2008/2009 (although we had a very strong El Nino in 2010). If one looks at the GAT, these dates appear to be turning points.

      A 2 or 3 year shift sounds more like the effects of ENSO shift. Could the physical dominance of ENSO be coming out in your data? It has been my opinion that when the PDO is warm, the El Nino tends to be stronger and when the PDO is in the cool phase, the La Nina tends to be stronger so that over time there is an accumulative effect or rising or lowering global temperatures. Do you see this in your data?

    • North and South Pacific are only loosely connected, so called ‘oscillations’ are only apparent (there is no oscillator in either the North or South Pacific, according to the definition of the word), there is only a driver (of no fixed period) which perturbs the quasi-equilibrium.

    • David Douglass replied: “Answer: these data sets are detrended. Also I did an incomplete analysis with more indices and got essentially the same results.”

      Detrended SST anomalies of the North Pacific north of 20N are inversely related to the leading PC of that detrended dataset (the PDO), so I can’t see how the results would be similar, unless the sign of the variations do not alter the results of your analysis.

      • The sign or the variation doesn’t influence the analysis as it is based on the absolute values of the correlations.

      • Pekka Pirilä: Thanks. But while the detrended North Pacific SST anomalies are inversely related to the PDO, they are not mirror images:

        In fact, on decadal timescales, the detrended North Pacific SST anomalies lead the PDO by a number of years. I’ve inverted the scaled PDO in the following graph (data smoothed with 121-month filter):

        And that brings me back to my original question to David Douglass, why not use detrended North and South Pacific SST anomalies so that the analysis is comparing oranges to oranges (and not oranges to the pattern on the skin of the orange)?

      • Bob,
        Thanks for your additional comments. What you tell now came to my mind already when I wrote my previous comment, but I decided write it anyway, as it was relevant in connection to your previous formulation.

        The whole issue of mode switching in ocean circulations is very interesting, but I appear to agree with many others, when I feel that the evidence presented in existing scientific literature is not convincing. It is using the limited set of indices that we have and mining for signal from that set. It appears more likely that they find in this way something spurious than real, even if some important mode switching processes do indeed exist. The data may just be insufficient for finding the real processes or at least giving convincing evidence that, what has been observed is significant.

      • Paul Vaughan

        Pekka, if you study enough of the indices using complex methods, you will find compelling evidence of external global drivers (with distinct local manifestations that get scrambled by anthropomorphic windowing parameters). This is not a simple matter to discuss.

      • Mr. Tisdale
        Delay on your graph is about 4 years, Di Lorenzo from Dr. Curry’s GTec quotes 3 year delay between the North Pacific Gyre (NPG) oscillation (Californian side) and the Kuroshio jet.
        I’ve been collecting data for various events along the NPG’s path and found number of delays between 2 and 40 years PDO relative. However I can’t find a reliable estimate of the time the NPG takes to complete one full orbit. Any ideas?

      • vukcevic: Sorry. No idea.

  25. Paul Vaughan


    Douglass, D.H. (2010). Topology of Earth’s climate indices and phase-locked states. Physics Letters A 374, 4164-4168.

    Click to access Topology_PLA20011.pdf

    The most important sentence from the article:

    “The 84-month window in the computation of the correlation coefficients should also be varied.”

    However, without lucid awareness of the key point made by Schwing, Jiang, & Mendelssohn (2003) [well before Tsonis, Swanson, & Kravtsov (2007), who have been mistakenly identified as the pioneers of this file] about aliasing off nonstationary spatial modes, Douglass (2010) could be leading already-lost people yet further astray.

    Schwing, F.B.; Jiang, J.; & Mendelssohn, R. (2003). Coherency of multi-scale abrupt changes between the NAO, NPI, and PDO. Geophysical Research Letters 30(7), 1406. doi:10.1029/2002GL016535.

    Click to access 2002GL016535.pdf

    In a nutshell:
    Aggregation criteria affect summaries of spatiotemporal pattern. In particular the effect of integration across spatiotemporal harmoncis cannot be ignored. The mainstream convention of considering only grain – while completely ignoring extent – is like insisting that only magnification – and not focal length – is key for establishing sharp vision. We have here a collective failure (by the vast majority of the mainstream establishment) to recognize the FUNDAMENTAL effect of spatiotemporal windowing parameters on statistical summaries. Such fundamental errors MUST be corrected without further delays.

    All responsible leaders (particularly those from the fields of advanced physical geography &/or spatiotemporal sampling theory) who understand the preceding are encouraged to consider the possibility that they have an ethical duty to assertively enter the climate discussion to assist with the necessary corrections before fundamentally flawed vision is allowed to naively lead society & civilization further astray.

    As a final note, Douglass (2010) should also consider using multiscale complex correlation (i.e. with both real & imaginary parts, based on adjacent derivatives) as a superior alternative to promoting potentially very seriously misleading statistical lags.

    • P. Vaughan,

      Statistical lags do need to be handled with care. Do you have an online primer you would recommend for multiscale complex correlation of time series?

      Multiscale Analysis of Complex Time Series: Integration of Chaos and Random Fractal Theory, and Beyond, is not in my budget right now.

      • Paul Vaughan

        Dallas, no, but here’s a brief video of a simplified version of the problem:

        Also, some strategic background reading:

        1) Sidorenkov, N.S. (2005). Physics of the Earth’s rotation instabilities. Astronomical and Astrophysical Transactions 24(5), 425-439.

        Click to access 425-439.pdf

        2) Gross, R.S. (2007). Earth Rotation Variations – Long Period. In: Herring, T.; & Schubert, G. (eds.) Treatise on Geophysics, Volume 3 (Geodesy), 239-294.

        Best Regards.

      • Thanks Paul, I have seen that, neat! Have you read Tsonis’ paper on teleconnections using the lower troposphere pressures? It gives a fair idea of the number of metronomes.

      • Paul Vaughan

        My current guess: The number of primary oscillators is 2 or 3. I’m not as taken by Tsonis, Swanson, & Kravtsov (2007) as many are, but the contribution has played a useful role in strategically refocusing discussion.

        In a nutshell, complex correlation involves matrices of correlations of multiscale adjacent derivatives of series (with each cell having both real & complex parts). Elaboration would be grossly impractical via this forum & medium. Most of the climate literature only subtly touches on the tip of the iceberg of what is possible — not entirely sure why, but it’s plain to see that the result has been catastrophic derailment by [the spatiotemporal version of] Simpson’s Paradox.

        Apologies for the outdated Gross (2007) link above — an alternate (slightly different version of the paper):

        Gross, R.S. (2007). Earth rotation variations – long period. In: Herring, T.A. (ed.), Treatise on Geophysics vol. 11 (Physical Geodesy), Elsevier, Amsterdam, in press, 2007.

        Click to access Gross_Geodesy_LpER07.pdf

        Click to access Gross_Geodesy_LpER07.pdf

        Everyone needs to get up to speed on Earth Orientation Paramters (EOP) in order for the climate discussion to be begin advancing.

        Best Regards.

      • Thanks for the link. It will take me some time to wrap my head around it enough to do me much good.

    • Tomas Milanovic


      I agree and mentioned your point in my post too.
      Would have been interested by the paper you referred but the link appears broken to me.

      • Tomas Milanovic

        This one is paywall but I found it free here :

        Click to access jianmenschwfrae02.pdf

        It is indeed a kind of Douglas method generalised to multiple window scales.
        Basically the method is mining in the data for strong variation in average and SD by trying all windows lengths from 2 to N/2 , N being the number of points.
        Of course it is also assumed that spatial patterns are stationary (not likely) and is restricted to 3 indexes.
        However the method would work for any number of indexes too .

        It finds also “climate shifts” but the added value here is that it includes the notion of time scale – it is surprising that Douglas didn’t use this paper which predates his by 7 years !

        Globally one could chain produce this kind of papers by taking the Schwing’s method and applying it on P indexes chosen among N .
        One could even produce one’s own indexes and every new combination of indexes gives a paper :)
        The problem being of course not in the paper’s content but in the way how one chooses P among N , N being large.

      • I think that PDO and AMO are dominant indicators , since they are result of the same forces , except that the North Atlantic responds differently to the N Pacific. Statistical analysis is fine as long as the cause and consequences are known; not a case with the current understanding.

      • Paul Vaughan

        The link you gave goes to the wrong paper. Can you share the correct link? (I would appreciate an opportunity to update my link records — so thanks if so.)

    • Perhaps a very good statistician would look this over and validate the soundness in these types of applications – it certainly looks promising. The situation with non-linear oscillators is a little complicated, since the oscillators can lock in on fundamentals and harmonics, as well as the obvious frequency pulling. That leads to one of my potential issues with averaging – high frequency components are lost. On the other hand, if lower frequency components can be found, harmonics can be studied. This may or may not lead to the discovery of smaller oscillators which couple at higher frequencies (higher harmonics).

      • Paul Vaughan

        Harold, please be careful with your misconceptions about the effect of averaging. I have provided some links for Dallas upthread; I also recommend them to you. I would also caution you about consulting statisticians who deal almost exclusively in the abstract.

  26. Synchronisation by itself is not sufficient to establish a climate shift. The synchronization and subsequent destruction of the synchronous state occurs at the time of observed climate shifts – that is, shifts in the trajectory of global surface temperature and ENSO frequency and intensity in particular.

    From the Tsonis et al 2007 paper –
    ‘This (1970’s) state is followed by an increase in coupling strength and incredibly, as in the cases of 1910 and 1940, synchronization is destroyed (at the time marked by the right vertical line) and then climate shifts again. The global temperature enters a warming regime and El Ninos become frequent and strong. The fact that around 1910, 1940, and in the late 1970s climate shifted to a completely new state indicates that synchronization followed by an increase in coupling between the modes leads to the destruction of the synchronous state and the emergence of a new state.’ We include the 1998/2001 shift from the 2009. However – these shifts are observable in real world data and not just inferred from topological considerations.

    The Douglas and Know 2009 paper use ocean heat content to discern climate shifts – and come reasonably close.

    The 1945 shift is commonly attributed to sulphate emissions – although this is only one side of the aerosols question and it does have quantified associated changes in the PDO and ENSO – the major factors in interannular to decadal changes in hydrology and cloud cover. And – one would assume – a major influence on decadal surface temperature change.

    Just on sulphates – black carbon seems more active in 3 ways (as aerosols, in albedo changes due to the dirty snow effect and through mixing in the atmosphere) and a decrease in sulphates should be offset against an increase in black carbon.

    Of relevance is the mixing of black carbon and sulphate in the atmosphere. Black carbon is higher concentrations captures reflected light from sulphates. Reduction of black carbon indeed provides by far the simplest means of increasing energy loss (0r reducing energy gain) from the planet while at the same time improving health and saving lives.

    ‘Sulphate strongly reflects solar radiation, whereas BC strongly absorbs solar radiation. Thus the net radiative forcing is determined by the relative amounts of BC and sulphate. However, BC is invariably internally mixed with sulphates and solar absorption by BC is amplified when it is internally mixed with sulphates. Such mixtures of absorbing and scattering aerosols (including other particulate matter such as nitrate, potassium and so on) are referred to as ABCs, for atmospheric brown clouds.’

    Click to access pr176.pdf

    To get back to the paper in hand – there is not sufficient justification in the topological analysis by itself to warrant calling a climate shift. There needs to be observable evidence of a shift in a climate parameter.

  27. Paul Vaughan

    I see no evidence that anyone here gets the main point Schwing, Jiang, & Mendelssohn (2003) made.

    • Tomas Milanovic


      Well it is not like Schwing&al can make many points in a 3 page paper.
      The main result being, I quote :

      “Multidecadal climate variability in the north Pacific atmosphere and ocean is strongly coupled….. We suggest that the fundamental atmospheric wave number varies on decadal scales and switched from a pattern where the Atlantic and Pacific were in phase prior to 1957, but out of phase during 1962-1988.”

      As that is what they write, I assume that this is the point they want to make.
      The method they use and which I described above, mildly supports the point.
      I wouldn’t say that this is anything very fundamental and beside the method which “objectively identifies changes in the time series by calculating contrasts between subsets of the data (Jiang 2002)” there is not much more.

      If you see some important point that would be hidden in these 3 pages and that everybody missed, what are you thinking of?
      Especially what is original in Schwing&al 2003 results with regard to the idea that different indexes are coupled which is as old as the indexes and that there are dozens of statistical methods to explore such couplings?

      • Paul Vaughan

        As Milanovic points out, methods are a dime a dozen and simple linear factor analysis (e.g. PCA, EOF, etc.) can’t sufficiently reduce the complexity.

        The cherished assumption of independence (which underpins conventional statistical inference) is absolutely untenable in a simple linear framework. As Milanovic has also emphasized, global oscillations have distinct local manifestations. The mainstream is not presently prepared to understand the nature of interannual terrestrial oscillations…

        An exercise for readers:
        Imagine that the centre of a multiscale temporal boxcar kernel is drifting (from beyond your control) left & right, sometimes by pi radians. What would be the effect on phase & amplitude stats? It may be paradoxical for some to imagine that such appearances, while possibly suggestive of the nature of complex phenomena, are not the reality; the spatial domain is not necessarily locked (e.g. in phase & wavenumber) by an anthropomorphic windowing parameter.

        Most climate discussion participants are absolutely ignorant of the effect of integrating across harmonics (even in a context where the summarizing window is just temporal & phase-locked to a simple wave-train).

        Misinterpreting multiscale spatial phase reversals as temporal features is a seriously FUNDAMENTAL error.

        Schwing, Jiang, & Mendelssohn (2003) is just an example to get readers thinking about this; their paper only subtly touches the tip of an iceberg, but it does so succinctly.

      • Tomas Milanovic

        Misinterpreting multiscale spatial phase reversals as temporal features is a seriously FUNDAMENTAL error.

        Yes I agree with that and it is the first reason for my guest post here (spatio-temporal chaos).
        The second being to try to expose some of the modern tools that are able to deal with complex non linear dynamics so that those who still think in terms of 19th century linear equilibrium concepts realize that there is a whole world beyond the simplist equilibrium paradigms.

        But how can you avoid the error you mentioned when at least 90% of the climate “science” is just randomly picking some statistical analysis method and apply it on series dependent on time only?

        Spatial averaging (which destroys any spatial patterns) is the alpha and omega of most studies .
        Even the Schwing paper uses arbitrary “indexes”.
        To be fair they at least explicitely add the hypothesis that “the dominant spatial patterns are stationary on decadal time scales”.
        Not that I believe one second that this hypothesis is true.

        Btw I also share your comment on EOF. When applied on poorly understood systems, the results tell more about the arbitrary spatial domain shape chosen for the study (e.g circle , square , spherical section etc) than about the process studied.

      • Paul I agree with every point you are making. Windowing is a tricky situation. By adjusting the windowing (in an unbiased manner), can’t you get a basic idea of what may be happening?

      • Paul Vaughan

        Dallas asked, “By adjusting the windowing (in an unbiased manner), can’t you get a basic idea of what may be happening?”

        Indeed – which is why I say the papers being discussed only subtly touch the tip of an iceberg.

        Some of the results awaiting mainstream attention are clean & simple – e.g. see here:

        It doesn’t end there.

  28. Synchronisation and phase locked loops between N Atlantic and N Pacific are a bit of nonsense.
    There are two independent drivers with different intensities and the time lines.
    Synchronisation and phasing are terms which can be correctly applied only to periodic functions; not the case here.

    • Paul Vaughan

      Are you thinking spatiotemporally? Or just temporally? (i.e. try not to overlook spatial phasing …and the concert of spatial & temporal phasing…)


      • It is space and time integration, so it must be the first rather than the second. The first differential of the NA driver, as well as the de-trended data gives also good correlation (see the last graph in ).

      • Paul Vaughan

        I recognize your “North Atlantic Driver (first differential)” with crystal clarity. Looks like you’ve been reading Sidorenkov & Leroux (& possibly Barkin). I encourage you to differentiate between PDO & North Pacific SST in your studies. The Earth Orientation Parameters (EOP) crowd is well ahead of the climate crowd on this file. You might also want to take a look at Gross (2007); you will find suggestions there that are compatible with Jackson’s ideas (& hence yours).

      • Climate science’s preoccupation with the minor CO2 effects is hampering progress towards understanding reality; it is detrimental to putting this new branch of science on a solid footing. Ideological entrenchment is hardly going to make room for alternative or lead along path of progress.

    • I am not sure this is really relevant, but smaller oscillations like the AO have a large impact on global temperature as it is determined. Yes, unusual flips like recently have a noticeable impact, but normal oscillation is not considered as important as it should be in my opinion. Is that wrong thinking?

      • Let me try to explain myself a little better. I notice warming temperatures in the high latitudes have a slope of say 1 in 1 while cooling has a slope closer to 1 in 2. To get rid of the extra moisture added during a warming requires greater than normal precipitation events or a longer period of normal precipitation before the next shift.

  29. Paul Vaughan

    Tomas Milanovic,

    In attempting to correct my outdated link to Schwing, Jiang, & Mendelssohn (2003), you instead linked to this (also interesting) article:

    Jiang, J.; Mendelssohn, R.; Schwing, F.; & Fraedrich, K. (2002). Coherency detection of multiscale abrupt changes in historic Nile flood levels. Geophysical Research Letters 29(8).

    Click to access jianmenschwfrae02.pdf

    Can you please share the correct current link which you found to the former article?

    Schwing, F.B.; Jiang, J.; & Mendelssohn, R. (2003). Coherency of multi-scale abrupt changes between the NAO, NPI, and PDO. Geophysical Research Letters 30(7), 1406. doi:10.1029/2002GL016535.

    Note: Readers may find the Nile-Pacific coherence of interest in Jiang, Mendelssohn, Schwing, & Fraedrich (2002).

  30. Tomas Milanovic


    Yes, it is this : .

    Btw you could look up Fraedrich (the same like the one from the Nile paper that I mistakenly linked) who has written many interesting papers from the dynamical point of view .
    One of the most cited is :

    It is an attempt at using standard chaos theory tools on the weather/climate “attractor” and he finds a low dimensionality e.g temporal chaos.
    It is neither the place nor the time to criticize the paper (and it can be substantively criticised) but it is interesting from the paradigmal point of view.